Equation of the Line
Let's use the following variables:
x = pounds of sugar
y = pounds of strawberries
Angela spent a total of $19.40 to make strawberry jam, thus:
1.80x + 2.50y = 19.40
The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.
The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:
For x = 0, solve for y:
1.80*(0) + 2.50y = 19.40
y = 19.4 / 2.5 = 7.76
This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.
For y = 0, solve for x:
1.80x + 2.50*(0) = 19.40
x = 19.40 / 1.8 = 10.78
This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.
Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).
If we substitute x = 8, y = 2:
1.80*(8) + 2.50*(2) = 19.40
14.4 + 5 = 19.40
19.40 = 19.40
The equation is satisfied, thus, the answer is:
Point B
